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<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  =  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">$1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relset_1.html#K9" title="RELSET_1:func.9">|</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c3">m</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:63_1_1"/><i><font color="Green" title="E34">A1</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c3">m</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive" title="b1">a</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></i>
<a NAME="E3:63_1_1"/>
<font color="Maroon" title="c3">m</font> is   <a href="monoid_1.html#NM2" title="MONOID_1:NM.2">Multiset</a> of <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="monoid_1.html#T28" target="_self" title="MONOID_1:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E4:63_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="monoid_1.html#NM2" title="MONOID_1:NM.2">Multiset</a> of <font color="Maroon" title="c1">A</font> st <br/>for <font color="Olive" title="b2">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="monoid_1.html#K15" title="MONOID_1:func.15">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relset_1.html#K9" title="RELSET_1:func.9">|</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:63_1_1"><i><font color="Green" title="E34">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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